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(a) Give a formal definition of the first partial derivatives of the function f(x, y), and its second order partial derivatives. (b) Using part (a), prove whether the following function f(x, y) is differentiable at point (0,0): ( , if r+ y, f(r, y) = 0, if r= y. (c) Assume that f is differentiable, and z = f(x² – y²). Show that dz dz ду [3,5,2]

(a) Give a formal definition of the first partial derivatives of the function f(x, y), and its second order partial derivatives. (b) Using part (a), prove whether the following function f(x, y) is differentiable at point (0,0): ( , if r+ y, f(r, y) = 0, if r= y. (c) Assume that f is differentiable, and z = f(x² – y²). Show that dz dz ду [3,5,2]

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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please assist with Differentiability of f(x, y) at point (a, b)

(a) Give a formal definition of the first partial derivatives of the function f(x, y), and its second order partial derivatives. (b) Using part (a), prove whether the following function f(x, y) is differentiable at point (0,0): 12–2y2 if 1+ y, I-y f(r, y) = 0, if r = y. (c) Assume that f is differentiable, and z = f(x² –- y²). Show that dz dz = 0 [3,5,2]
Transcribed Image Text:(a) Give a formal definition of the first partial derivatives of the function f(x, y), and its second order partial derivatives. (b) Using part (a), prove whether the following function f(x, y) is differentiable at point (0,0): 12–2y2 if 1+ y, I-y f(r, y) = 0, if r = y. (c) Assume that f is differentiable, and z = f(x² –- y²). Show that dz dz = 0 [3,5,2]
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